Re: On permittivity and permeability
- From: "Ken S. Tucker" <dynamics@xxxxxxxxxxxx>
- Date: 13 Oct 2005 13:07:35 -0700
Hey Timo great post!
Some things below...
Timo Nieminen wrote:
> In some recents posts, the claim was made that the permittivity and
> permeability of free space are zero, and that the concepts of
> permittivity and permeability are somehow intrinsically related to matter
> or ether.
>
> So, what ARE permittivity and permeability all about?
>
> Consider that the Maxwell equations:
>
> curl H - dD/dt = J
> curl E + dB/dt = 0
> div D = rho
> div B = 0
>
> contain 4 fields: E, D, B, and H, which, being 3D vector fields means that
> there are 12 unknown quantities. Since the 2 vector equations + 2 scalar
> equations only provides a total of 8 equations in vector components,
> something more is needed. Enter the consitutive relations:
>
> D = eE
> B = mH
>
> where e and m are the permittivity and permeability respectively. (We
> could also add J = sE, where s is the conductivity.) Finally, we have the
> Lorentz force law:
>
> F = rho E + JxB
>
> This can be read as a definition of E and B in terms of forces on charges
> and currents.
>
> From the Lorentz force law, we see that E must have dimensions of
> force/charge, while from div D = rho, D must have dimensions of
> charge/area. The permittivity of free space is essentially a conversion
> between these two quantities, so e has dimensions of
> charge^2/(force*area). One can of course choose units such that e0 has a
> numerical value of one, allowing it, perhaps unwisely, to be omitted from
> equations.
>
> Exercise: In the conventional SI choice of units, with E in V/m, show that
> e can be written in F/m. (That's farads/m; recall that Q=CV.)
>
> What if we have some matter around? The fields can result in an induced
> electrical polarisation in the matter. Note that dipole moment per unit
> volume has dimensions of charge/area, the same as D. So, the usual
>
> D = e0 E + P
I think Timo's "P" vector is equivalent to the polarization
tensor, just as E and B are F_0i and F_ij respectively, ok,
but P is fine, (as a density in GR).
Let's look at the "piezoelectric effect", where an applied
mass distorts the relations of a charge latice to produce
a voltage, that is the basis of electronic weigh scales
unless Timo likely understands better, but that's what I
understand.
In the presence of the Sun's "MASS" , light bends
(deflection) and slows down, (Shapiro), indicating
an alteration to "e" and "m" that seems to vary the
refractive index by the presence of matter, from
that PoV.
But this effect might also appear as a polarization,
due to mass, like the "piezo" does, you see Timo, GR
doesn't affix a certain mechanical reason to P, on
the contrary I think P indicates the presence of
matter, _even in a so-called vacuum_!
Anyway, that's why I think Timo's post is cool, and
I hope he will explain "piezoelectrical" voltage.
Regards
Ken S. Tucker
....
.
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